The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of $120$

millimeters of mercury $(mmHg)$ and standard deviation of $24.$

Someone qualifies as having Stage $2$ high blood pressure if their systolic blood pressure is $160$ or

higher. Stage $1$ high BP is specified as systolic BP between $140$ and $160.$

Give your answers rounded to $4$ decimal places.

a$.$ What is the probability that an adult in the USA has stage $2$ high blood pressure?

b$.$ What is the probability that an adult in the USA has stage $1$ high blood pressure?

c$.$ Your doctor tells you you are in the $30$th percentile for blood pressure among US adults. What is your

systolic BP$?$

$mmHg$

d$.$ What is the systolic blood pressure that cuts off the top $2\mathrm{.}5\%$ of adults in the USA?

$mmHg$